Number of Tennis Balls to make a 4 sided pyramid of 25 levels

Answer : 5525 Balls

Start from the top of the pyramid. For a pyramid of 1 level - Number of Tennis balls required is 1 For a pyramid of 2 level - Number of Tennis balls required is 1 + 4 For a pyramid of 3 level - Number of Tennis balls required is 1 + 4 + 9 For a pyramid of 4 level - Number of Tennis balls required is 1 + 4 + 9 + 16 How do you go about doing this is each level of N balls requires N+1 balls as support in the case of 2 dimensional pyramid, since this has 3 dimensions, each N2 ball requires support from (N+1)2 , therefore there would be N2 Balls in Nth level where N is 1,2,3,4... 25. So the answer here is 12 + 22 + 32 + 42 + 52 + .... + 252 Using this formula to calculate the sum of squares of first N integers Sum of squares of first N integers, we can calculate the number of balls requires as

(25 x (26) x (51) ) / 6 = 5525

10 Dec, 2009
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